Population genetics aims to understand the patterns of genetic variation, the forces that shaped our genome, and the evolution of our genome through time. The increasing ease to sequence the entire genome of a large number of individuals will answer some of these fundamental questions. Insights gained from population genetics will in turn fuel the design and execution of genetic mapping studies. Due to their special demographic histories, a single resequencing study can capture the greatest amount of genetic variation in isolated populations such as the Finns or the Sardinians. Thus, these populations are likely to be the most informative for population genetic questions in the first wave of large-scale whole-genome resequencing efforts. Moreover, because the patterns of rare variants are tightly related to the demographic history of the population, understanding the demography is essential for studying the genetic contribution of rare variants to complex traits and diseases. This is particularly pertinent in light of the limited success of genome-wide association studies to explain the genetic contribution attributable to common variants. Moreover, demography is not the only population genetic process that influences the patterns of genetic variation. The mutation rate, the rate at which new variants are introduced to the human population, is another important force that shapes the human genome. Knowing the mutation rate specific to a population and/or to a local genomic region will enable accurate modeling of the null expectation of rare variant distributions and proper testing of the association of a genomic locus to a disease or trait. Furthermore, an accurate estimate of the mutation rate would more broadly impact genetics and evolutionary biology, such as inferring the divergence time between species. However, current approaches for estimating mutation rates are either based on limited pedigrees or dependent on an accurate evolutionary model. In the present proposal we aim to develop approaches that will investigate the population genetic, demographic, and disease genetic properties of a population. Specifically, we will develop a novel approach to estimate mutation rates that complements current approaches and is independent of the population demography. Secondly, we will extend an existing method of demographic history inferences to scenarios involving interactions between multiple populations. Finally, we will test the efficacy of genetic mapping studies specifically designed to take advantage of the unique demography of isolated populations. In each case, we will first develop and test our methods on simulated datasets, and then apply them to the dataset of Sardinians, one of the largest existing whole-genome resequencing datasets of an isolated population. Notably, our framework will not only help us understand the history of Sardinia, but can also be extended to other outbred and potentially diverse populations as these datasets become available.